We develop several critical concepts that should be considered when interpreting, modelling and designing future experiments for flows over sloping terrain. Vertical buoyancy fluxes in katabatic flows can be positive and a source of turbulent kinetic energy (TKE) despite the statically stable, thermal stratification that drives these flows. This phenomenon occurs when the ratio of along-slope to slope-normal kinematic heat fluxes is greater than the cotangent of the slope angle, suggesting a critical value of slope-angle steepness found in earlier studies. We provide field-data-based evidence that the along-slope heat flux may dominate the variables in this inequality, and therefore in generating buoyant TKE production or suppression over a steep slope. These data show the along-slope heat flux can be more variable and significantly larger in magnitude than the slope-normal component. The gradient Richardson number does not include the effects of the along-slope buoyancy; furthermore, none of the canonical stability parameters can properly reflect the TKE redistribution from turbulent transport divergence and the sink of TKE in cases of counter-gradient momentum fluxes, which we frequently observe near the peak of the katabatic jet. In such cases, canonical stability parameters inadequately represent the physical mechanisms associated with stability. These results have broad implications related to accurately modelling turbulence and surface exchanges over sloping terrain and illustrate the need to more thoroughly investigate the along-slope heat flux and its drivers, the meaning and definitions of stability, and the effects of non-local turbulent transport.